Answer
domain: $(-\infty, +\infty)$
range: $(-\infty, +\infty)$
Refer to the graph below.
Work Step by Step
Find the x-intercept by setting $f(x)$ or $y$ to zero, then solve for $x$.
$f(x) = \frac{1}{2}x-6
\\0=\frac{1}{2}x-6
\\0+6=\frac{1}{2}x-6+6
\\6=\frac{1}{2}x
\\2(6)=2(\frac{1}{2}x)
\\12=x$
The x-intercept is $(12, 0)$.
Find the y-intercept by setting $x=0$ then solving for $y$.
$f(x)=\frac{1}{2}x-6
\\f(x) = \frac{1}{2}(0)-6
\\f(x)=0-6
\\f(x)=-6$
The y-intercept is $(0, -6)$.
Plot the intercepts and connect them using a line. The point $(4, -4)$ can be used as a check point.
(Refer to the graph in the answer part above.)
The graph covers all x-values and all y-values.
Thus, the given function has:
domain: $(-\infty, +\infty)$
range: $(-\infty, +\infty)$
